Spatial estimation of geologic data requires extension of their properties from limited area to field scale using small amount of sample data. Therefore, scaling law, which relates data statistics at different scales, is indispensable to obtain detailed spatial model over wide area. This paper presents a method suitable to spatial estimations at different scales, and proposes a new combination of scaling laws for the data distribution and semivariogram. As a fundamental examination, DEM (Digital Elevation Model) of the Aso caldera area (20 X 20 km²) in central Kyushu, southwest Japan, was applied to a problem that estimates a distribution at fine scale from a coarsely arranged data set. Scaling laws on the data histogram and the semivariogram parameters (sill, range, and nugget effect) were identified by changing the data interval of the DEM. First, ordinary kriging, sequential Gaussian simulation, and two neural network based methods were used for producing 250-m DEM from the 1000-m DEM. Local peaks and small valleys could not be reconstructed by these methods due to mainly smoothing effect. On the contrary, simulated annealing (SA) method, which adjusts the semivariogram of data selected randomly from the histogram at the target scale to the defined semivariogram model, was more effective for that spatial estimation. Thus, SA was adopted for pore spatial simulation in homogeneous porous media using bubble cement material samples. Pore distribution models at largely different scales from 1 X 1 cm² to 5 X 5 m² were obtained using the two scaling laws on the pore radius and semivariogram. Although the porosity is fixed, pores are connected largely with the increase of area size. This simulation result is available to examine strong influence of pore connectivity on hydraulic conductivity, which contributes to interpret the scale effect of hydraulic conductivity. The proposed method was also applied to a Berea sandstone sample for pore simulation at microscopic area size to core sample size. Changes in the average and variance of volume of connected pores with the size were characterized.

View full abstract